One fuel injector (DE 10 2004 002 134 A1) has a hydraulic coupler, which is situated in a valve assembly that is accommodated in a valve housing; the valve assembly is made up of a valve needle controlling an injection orifice and a piezoelectric or magnetostrictive actuator actuating the valve needle, the coupler being supported in force-locking manner on the valve needle and actuator via a separate gimbal bearing in each case. The hydraulic coupler compensates for length differences resulting from different expansions of the valve housing or valve needle and actuator caused by temperature fluctuations, so that no gap can form between valve needle and actuator and it is ensured that the full lift of the actuator is transmitted to the valve needle in a 1:1 manner at all times. The hydraulic coupler has a housing cup including a cup bottom, a cup shell, and a cup opening as well as a piston which is guided in the housing cup in axially displaceable manner; a fluid-filled coupler gap exists between the piston and cup bottom, and an annular gap exists between the piston and cup shell. An annular first diaphragm is fixed in place on the cup shell via its outer diaphragm edge, and on the piston via its inner diaphragm edge; it seals the annular gap between the cup shell and piston in the cup opening while encompassing a first fluid-filled compensating chamber. A second diaphragm, situated on a side of the cup bottom facing away from the piston, together with the housing cup surrounds a fluid-filled second compensating chamber, which is connected to the coupler gap on one side by way of a throttle bore, and to the first compensating chamber on the other side by way of a connecting channel which axially runs through the piston. The coupler gap and the compensating chambers are filled with fluid, e.g., hydraulic oil, via a hermetically sealable fill channel, which, for example, is realized by a radial bore that is introduced in the cup shell and discharges into the connecting channel between the first and second compensating chamber.